+1234 A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.
+129852 The side of the hexagon = (1/6)p
1/6 of the area is a triangle with sides of (1/6)p and an included angle of 60°
So
(1/6) (3/2) = (1/2) [(1/6)p]^2 (sqrt (3) / 2)
1/4 = (1/4) (sqrt (3)) / 36 p^2
1 = [ sqrt 3] / 36 * p^2
p^2 = 36 / sqrt (3)
p = 6 / 3^(1/4)
side = (1/6) * 6 / 3^(1/4) = 1 / 3^(1/4) ≈ .76
